Optimization of Number Representations - Signal Processing Systems - page 1279

Optimization of Number Representations

Wonyong Sung

Abstract In this section, automatic scaling and word-length optimization
procedures for efficient implementation of signal processing systems are explained.
For this purpose, a fixed-point data format that contains both integer and fractional
parts is introduced, and used for systematic and incremental conversion of floating-
point algorithms into fixed-point or integer versions. A simulation based range
estimation method is explained, and applied to automatic scaling of C language
based digital signal processing programs. A fixed-point optimization method is also
discussed, and optimization examples including a recursive filter and an adaptive
filter are shown.

1 Introduction

Many embedded processors do not equip floating-point units, thus it is needed
to develop integer versions of code for real-time execution of signal processing
applications. Integer programs run much faster than the floating-point versions,
but integer versions can suffer from overflows and quantization effects. Converting
a floating-point program to an integer version requires scaling of data, which is
known to be difficult and time-consuming. VLSI implementation of digital signal
processing algorithms demands fixed-point arithmetic for reducing the chip area,
circuit delay, and power consumption. With fixed-point arithmetic, it is possible
to use the fewest number of bits possible for each signal and save the chip area.
However, if the number of bits is too small, quantization noise will degrade the

W. Sung ( )
Department of Electrical and Computer Engineering, Seoul National University,
599 Gwanangno, Gwanak-gu, Seoul, Republic of Korea
e-mail: [e-mail]